Question

Psychologist Michael Cunningham conducted a survey of college women to see whether, upon graduation, they would prefer to marry a high school teacher who has short workdays, summers off, and spare energy to help raise children, or a surgeon who earns eight times as much but works brutal hours. He found that 75% of the college women said they would choose the teacher. [Source: Alex Williams, “Putting Money on the Table,” The New York Times, September 23, 2007.]

Select the appropriate distribution in the Distributions tool to help answer the questions that follow.

Nate is single and completing the last year of his surgical residency at Brown Medical School. He decides that it’s time to get married and embarks on a mission to find his soul mate. His strategy is to select 10 female college graduates randomly and take each prospect on a date sometime during the next 2 months. Let X denote the number of Nate’s dates who prefer surgeons.

The probability that exactly four of Nate’s dates are women who prefer surgeons is_________

The probability that at least six of Nate’s dates are women who prefer surgeons is__________.

The expected value of X is _________ , and the standard deviation of X is_________ ?

Answer 1

(The probability values have been rounded to four decimal places.)


10-X Ginen, n= sample size = no. of randomly selected female college graduates who are Nate's dates = 10. b= prob. of preferring surgeon = 25% = 0.25 X ~ Binomial (n=10, P=0,25) The pmfos X= P(X=X) = 10 1 10.25)2 10.75) "°* ; *= 0, 1,0. (;) Prob. (exactly 4 profer swyrons ) = P(X=4) = 10.1460] (ii) Prob. (at least 6 proses sugions) = P(X76) = 1-P(+26) al-P(x 5) = |-Plx = 0) to ..+ P(x =5)] = 0.019 7). (ii) expected value = E(X) = np = 2,5]. a scapated Standard deviation = Supli-p) = 11.3693 La CamScanner